Bi-Duality in Dynamic Systems

Abstract

From static equilibria to dynamical problems, this chapter presents the subject of duality theory for convex Hamiltonian systems. The framework for dynamics is the same as that for static systems, but, the duality theorems are more interesting.

Keywords

The Lord God said, “it is not good for the man to be alone, I will make a helper suitable for him.” ... Then, the Lord God made a woman from the rib he had taken out of the man, and brought her to the man.”

I—Genesis, II

Opposition is how the Tao moves; Weakness is the means the Tao employs. All things are born from Something and Something from Nothing.

I—Lao Chi

A great truth is a truth whose opposite is also a great truth.

I—Niels Bohr

It is a splendid feeling to realize the unity of a complex of phenomena that by physical perception appear to be completely separated.